Problem: Which of the following numbers is a factor of 80? ${3,9,10,13,14}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $80$ by each of our answer choices. $80 \div 3 = 26\text{ R }2$ $80 \div 9 = 8\text{ R }8$ $80 \div 10 = 8$ $80 \div 13 = 6\text{ R }2$ $80 \div 14 = 5\text{ R }10$ The only answer choice that divides into $80$ with no remainder is $10$ $ 8$ $10$ $80$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $10$ are contained within the prime factors of $80$ $80 = 2\times2\times2\times2\times5 10 = 2\times5$ Therefore the only factor of $80$ out of our choices is $10$. We can say that $80$ is divisible by $10$.